This will be a Phase II, multicenter, open-label study to establish the ability of VX-710, given in combination with paclitaxel, to overcome clinical drug resistance in women with advanced breast carcinoma who have had documented progressive disease following treatment with paclitaxel. Patients must have received prior chemotherapy with at least two courses of paclitaxel prior to beginning on the study. Patients will be treated with VX-710 by continuous IV infusion over 24 hours. Paclitaxel will be administered over 3 hours and will be started 4 hours after the start of VX-710 infusion. This regimen will be repeated at intervals of 21 days until evidence of disease progression, intolerable adverse events or withdrawal of patient consent.